and the host of similar terms received their several perplexing significations,-and why there is neither order, nor similarity, nor analogy existing among our tables, though it is evident, from the arbitrary character of the entire nomenclature, that all three might easily have been obtained. The vices of an imperfect system are only to be understood by comparison with a good one, and we shall therefore content ourselves with a brief inquiry into the fundamental difficulty attending the construction of such tables; and also a brief description of that system whose introduction is recommended into this country, because it meets that difficulty in the simplest and most effectual manner.

Numbers can, as we all know, be very easily applied to distinct objects, simply because they are distinct and separate, each being called one; but, before we can make use of our arithmetic, to describe a road of a certain length for instance, we must have determined some one length which shall be called one, and be taken as the standard. How shall such a length be found? There is no natural object which can be universally referred to, and which is always of the same dimensions. Length itself is a magnitude capable of continued increase or diminution, without break or interval, while arithmetic can only represent such increase or diminution as is gradual, i.e., step by step, and must always leave the intervals between those steps unexpressed. Length, therefore, is a magnitude different in kind from number, and no mere system of numbers can adequately represent all the possible relations of different lengths. The same remark will apply to time, to weight, to bulk, to surface, and to value, all of which are magnitudes whose law of extension is totally different from that of number, and in relation to which the choice of a unit must be wholly arbitrary. In regard to one of these magnitudes, however, the selection of the unit is taken out of our hands, for nature marks off certain equal periods of time with great exactness; and whatever subordinate arrangements we may choose to make as to centuries, lustrums, weeks, calendar months, hours, and minutes, they must all be founded on the day or the year, as the only standards we possess. In this one department science cannot interfere, and a Decimal Time-Table is therefore neither desirable nor possible.

Long Measure.-In the selection of a fixed unit of length, unalterable in its nature, and recoverable by physical investigation even if all the standard measures were destroyed, two courses are open to the man of science. The one is to ascertain the exact size of our own earth, and to select a certain aliquot part of its circumference as the standard of all linear measure. The other is to take the length of a second's pendulum to serve that purpose. The fact that, under certain physical conditions, all pendulums which vibrate in a given time are of exactly the same length, added to the fact that time is measured for us by nature (a minute or a second being a known and exact fraction of a day), enable us to use the pendulum, if not as a standard, at least as a means of verifying our standards of length.*

Of these two methods, the French Government in 1791 adopted the former. The learned men, to whom was entrusted the duty of determining the standard, were Méchain and Delambre, and their conclusions have been subsequently verified by Arago and Biot. They measured a degree of that meridian which passes through Dunkirk, Paris and Barcelona, and thus calculated the entire length of the line from the pole to the equator. A ten-millionth part of this length, or a forty-millionth part of the entire circumference of the earth, is the French metrical unit. It is called a mètre, and measures about 39.371 English inches.

The terminology employed in all the tables of weights and measures is the same.

* A second's pendulum in the latitude of London, vibrating in a non-resisting medium, and at the level of the sea, measures 391393 inches. A recent Parliamentary Commission, in reporting to the Crown on this subject, states, however, that "We consider the ascertaining of the earth's dimensions, and of the length of a second's pendulum in terms of the standard of length, as philosophical determinations of the highest importance, to the prosecution of which we trust her Majesty's Government will always give their most liberal assistance, but we do not urge this on the Governnient at present, as connected with the conservation of standards."

Syllables are adapted from the Greek and Latin languages to express the decimal multiples and subdivisions of the unit, e. g. :

These syllables can all be prefixed to the word mètre, and hence a kilomètre is 1000 mètres; a décametre, 10 mètres; a décimètre, one-tenth of a mètre; and a centimètre, one hundredth of a mètre, &c., &c.

The first duty of a French schoolmaster on this point is to make the fundamental conception of a mètre perfectly clear to the children. To this end, every school contains a staff or ruler of the exact length, properly graduated into tenths, hundredths, and thousandths, and copies of it, either in the form of rods or diagrams, are multiplied in every direction. He has next to explain the precise meaning of the prefixes we have just given, for they are applicable alike to all the other tables. The rest of the system is then easily learnt.

Superficial Measure.-Take a décamètre, i.e., a line measuring 10 mètres, and erect a square upon it; the square so described is the French unit of surface. It is called an are. As ten such squares would not of themselves form a square, only two of the prefixes of the foregoing table are needed in this case; e. g.,

Hect-are
Centi-are

=

100 ares, or the square of a hectomètre; and

the hundredth part of the are; or the square of the mètre. This is the table corresponding to our land measure, a hectare being about 2 English acres.

Solid Measure.-Take a mètre; form a cube having that length, for each of its edges. Each of the six faces will then be a square mètre, or a centiare. This magnitude is called a stère. It is the unit of bulk in the French system. A décastère consists of ten such volumes, a décistère of a tenth of such volume. The other prefixes are seldom used.

Liquid Measure.--Take a décimètre, or the tenth part of a mètre. Make a cube having this length for each of its edges. This magnitude is called a litre. It is the French unit of capacity, and is used for measuring corn and dry goods, as well as liquors. As in the former tables, we have here a kilolitre, or 1000 litres; a hectolitre, or 100 litres; a décalitre (10 litres); a décilitre, the tenth of a litre; a centiliire, a millilitre, &c.

Weight. Take a vessel in the form of a cube, having for each of its edges a centimètre, or one hundredth part of a mètre. Fill this vessel with distilled water at the maximum density. The weight of this volume of water is the French unit of weight. It is called a gramme, and is used alike for the precious metals, for drugs, for ordinary merchandise, and for all articles whatever which have to be weighed. The table of weights, therefore, includes a kilogramme, which is 1000 grammes; a hectogramme, or 100 grammes; a décagramme, or ten grammes; and the subdivisions of the unit, viz., a décigramme, or one-tenth; a centigramme, or one-hundredth; and a milligramme, or one-thousandth of a gramme.

Money.-Take a piece of alloyed silver, weighing exactly five grammes. Let it consist of nine-tenths pure silver, and one-tenth alloy. Its value is that of the franc, the basis of the French monetary system, and the unit of value. Words representing higher values than this are never used, as all large sums of money are calculated in francs; but the measures of the monetary unit harmonize with the rest of the system, a décime being one tenth, and a centime one hundredth of a franc.

It is enacted that all vessels in use for measuring liquids shall have a cylindrical form, the height being double the diameter. For dry goods, the diameter and the depth of the vessels are to be equal. Hence a realy method may be found for detecting fraudulent measures, as the precise dimensions of the standards in millimètres are stated in all the French books of arithmetic, and are generally known by the poor.

Such is the French Système Métrique. Its technical words are new and strange to English ears, and might probably be slightly altered with advantage, before they became quite naturalized among us. But it is by far the simplest and most beautiful system yet devised, and has advantages which ought to go far to reconcile us to the prospect of a social revolution, some temporary confusion and annoyance, and a serious interference with many deep-rooted habits and prejudices. It is thoroughly decimal, and disposes for ever of all the differences between simple and compound rules in arithmetic. It employs the same nomenclature throughout, and every word suggests its own meaning. There is a beautiful connexion also apparent among all the parts of the scheme, the measure of value being founded on that of weight, the measure of weight on that of capacity; and those of capacity and of surface upon the measure of length. This mètre, or linear unit, is thus the base of the whole system, and every detail in all the tables can be directly or indirectly referred to it.

It is observable that this system, if taken in its integrity, would involve the adoption of the French monetary unit, or franc, as the basis of our coinage and accounts. But there are many reasons which would render this step at least difficult and undesirable. Our own gold sovereign is far better fitted to be the basis of English money than any silver standard. Moreover, value is a fluctuating and uncertain thing, and differs essentially from each of the other magnitudes to which metrical tables apply. The connexion of the silver unit of value with the Système Métrique is somewhat arbitrary, and we should neither mutilate that system nor destroy any of its usefulness, if we were to adopt it as far as regards measures of length, surface, capacity, and weight only, retaining our own English standard of value, and decimalising from it. However this be ultimately determined, teachers of elementary schools will do wisely to watch the progress of this question, and to prepare themselves at least to give an intelligent hearing to any arguments on either side of the subject which may be brought before them.

ABSTRACT OF LESSON.

The following has been sent to us by a correspondent who accustoms his pupils to make notes of historical lessons during their delivery, and to prepare careful summaries of those lessons afterwards. The plan of requiring such exercises from the children is a very good one. It serves to fix their attention in the hour of instruction, to strengthen their memories, to furnish them with home employment, and to generate a habit of describing facts in appropriate and well-chosen language. It also enables the teacher to detect errors in spelling, and to dispense with separate exercises in dictation. The specimen given is an abstract of the matter contained in several lessons on the period of history to which it refers.

WARS OF THE ROSES, 1455 to 1485.

I. MAP OF ENGLAND, showing the position of each of the places mentioned in this portion of the history.

IV.-BATTLES, &C.

SUBJECTS FOR DISCUSSION AMONG TEACHERS.

We are sometimes asked to suggest topics suited for essays and discussions in meetings of teachers. It is not easy to suppose, however, that there can be any very general need of such suggestions. The best essays given in the numerous Associations which now, happily, exist in almost all parts of the country, are those suggested by the experience of the writers themselves, and not those which are prescribed to them by others. Every earnest teacher, who will watch his own successes and failures, and seek to know their causes, will be able to give a valuable paper at a meeting of his fellow-labourers, and is sure to interest them. The subjects for conference, on such occasions, should be sought in the schools; and all hints arising out of experience and observation so gained will always be welcome at a teachers' meeting; for it is in that way that a schoolmaster may best learn what is the sort of advice his brethren are likely to need, what are the special dangers and difficulties to which one who works by himself is exposed, and what are the points respecting which the experience of others will be most useful to him.

The proceedings at almost every Association of Schoolmasters comprise, we believe, first, the reading an essay; secondly, a friendly discussion on the subject to which it refers. It would, therefore, seem desirable that the theme of the essay be not only a suitable one for lecturing, but also a suitable one for discussion. Both are useful, though in different ways. The purpose of the essay is to bring a carefully prepared body of facts or arguments forward, to serve as a substratum to the conversation which ensues, and to define its limits. The purpose of the discussion is to elicit the results of manifold experience, to afford an opportunity for stating objections, and to promote sympathy and mutual helpfulness among the members. Of these two it may safely be said that, practically, the second is of far more importance than the first. For this is an essay-writing age; the ablest writers of our time communicate their thoughts to the world through the medium of periodicals, and there is scarcely a subject which interests teachers on which it would not be easy to point to some valuable article in a review or magazine, in which all that can be said, in the way of illustration, is said with clearness and force. Good essays on education are within every one's reach, and it is not, therefore, the main business of a Teachers' Association to provide them. But the comparison of experience, the friendly interchange of thoughts about school-management, and the confidential discussion of difficulties, are matters respecting which no periodical literature, however valuable, can supply the needs of the profession; and it is the special office of an Association to furnish help of this sort. We believe that the very large majority of those who attend such meetings regard the essay as, for all practical purposes, subordinate in importance to the conference which usually follows it.

If this be kept in mind, the choice of subjects on which to engage the attention of teachers at these rare and valuable opportunities for self-improvement, will become less difficult.

An essay, to serve the purpose thus indicated, should be rather suggestive than didactic, rather practical than theoretical, rather aiming at professional usefulness than literary merit. Its materials should be drawn rather from the study of children, their doings and their wants, than from books; and its main object should be to awaken inquiry, and to draw out the experiences of those who are assembled. However elaborately it may be finished as a composition, it must be regarded as unsuccessful if it fails to do this. If it only pleases and interests the hearers, it does no more than a well-written article in a magazine, which might be taken home and read in silence. Moreover, the topic on which it is easiest to write a good paper is not necessarily the one best suited for discussion in a teachers' meeting, and this should always be remembered before the point is decided.

The history of education during the last few years shows us that Societies which